Speaking to Nick Ferrari on LBC, Mr Farage said he wholeheartedly accepted - and wanted the other parties involved as well.

He said: "When the Deputy Prime Minister says he wants to go public and have a debate on this issue, I have absolutely no choice.

"I've got to say yes as we need to have a national debate on what I think is the most important issue that this country has faced for 100 years in terms of our constitution.

"The answer is YES. But with one small caveat.

"I do really want for the Labour party in the shape of Ed Miliband and the Conservative party in the shape of the Prime Minister to join this debate as well.

"So yes I'll do it with Nick Clegg, but the other two, I would like to see them there as well."

When asked what will happen if the two main parties reject the offer, Farage added: "Well, they will say no.

"Downing Street have already briefed, saying David Cameron is too busy running the country. Well, running probably is the right word.

"But actually Mr Cameron, that's what the debate is about. Who is running the country? Are you running it as the Prime Minister who goes to the House of Commons once a week or is EU Commissoner Viviane Reding right when she said in London last week that over 70% of our laws are now made in Brussels?

"I suspect that David Cameron does not ever want to have this debate. I think the splits in the Labour party over the European question have been highlighted by open-door immigration, which hasn't just put lots of young people out of work, it's led to wage compression.

"I suspect that they don't want to have the debate, so if it's Nick Clegg and I, let's have the debate.